Difference between revisions of "2006 AMC 10B Problems/Problem 2"
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== Problem == | == Problem == | ||
+ | For real numbers <math>x</math> and <math>y</math>, define <math> x \spadesuit y = (x+y)(x-y) </math>. What is <math> 3 \spadesuit (4 \spadesuit 5) </math>? | ||
+ | |||
+ | <math> \mathrm{(A) \ } -72\qquad \mathrm{(B) \ } -27\qquad \mathrm{(C) \ } -24\qquad \mathrm{(D) \ } 24\qquad \mathrm{(E) \ } 72 </math> | ||
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== Solution == | == Solution == | ||
+ | Since <math> x \spadesuit y = (x+y)(x-y) </math>: | ||
+ | |||
+ | <math> 3 \spadesuit (4 \spadesuit 5) = 3 \spadesuit((4+5)(4-5)) = 3 \spadesuit (-9) = (3+(-9))(3-(-9)) = \boxed{\textbf{(A)}-72}</math> | ||
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== See Also == | == See Also == | ||
− | + | {{AMC10 box|year=2006|ab=B|num-b=1|num-a=3}} | |
+ | |||
+ | [[Category:Introductory Algebra Problems]] | ||
+ | {{MAA Notice}} |
Latest revision as of 10:33, 19 December 2021
Problem
For real numbers and
, define
. What is
?
Solution
Since :
See Also
2006 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 1 |
Followed by Problem 3 | |
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All AMC 10 Problems and Solutions |
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